Applications of SHM

Another simple device besides the spring-mass that can produce simple harmonic motion is the simple pendulum. A simple pendulum consists merely of a point-mass (m) suspended from a fixed point by a rod or string of length (L). The mass of the rod or string is assumed to be so much less than the suspended mass that it can be ignored. If the suspended mass is displaced to the left or right, while the rod or string is kept firm, and then released, the mass will swing freely back and forth under the gravity’s influence. For small horizontal displacements the restoring force on the suspended is given by:

F=-mgsinϴ

Therefore acceleration: a=F/m = -mgsinϴ/m = -gsinϴ

If ϴ does not exceed about 10°, then sinϴ = s/L,

Due to this, the acceleration a=-(g/L)s = -(2πf)²s, where (2πf)²=g/L

So the object oscillates with simple harmonic motion because its acceleration is proportional to the displacement from equilibrium and always acts towards equilibrium.